knitr::opts_chunk$set( collapse = TRUE, comment = "#>", out.width = "100%" )
The fixedincome
package implements many interpolation methods for spot rate curve.
All interpolation methods inherits the S4 class Interpolation
.
Once you instantiate an Interpolation object, it has to be set to a SpotRateCurve object and this
is done throught the curve's interpolation<-
method.
There is a list with the interpolation methods implemented and their constructors:
interp_flatforward
interp_linear
interp_loglinear
interp_naturalspline
interp_hermitespline
interp_nelsonsiegel
interp_nelsonsiegelsvensson
interp_flatforwardcopom
(thru copom package)Here it follows an example on how to create and set an interpolation to a spot rate curve.
Let's start by creating a curve using data obtained with rb3 package.
Firstly, the packages have to be loaded.
library(rb3) library(dplyr) library(fixedincome)
In order to build a term structure formed only by futures maturities, the yield curve data and
futures data have to be mixed and this is done with the rb3::yc_superset
function.
Once the superset is returned, the rows related to futures maturities can be filtered.
The first term, usually 1 business day term, is also used to anchor the curve's short part.
refdate <- as.Date("2022-08-05") yc_ <- yc_get(refdate) fut_ <- futures_get(refdate) yc_ss <- yc_superset(yc_, fut_) yc <- bind_rows( yc_ss |> slice(1), yc_ss |> filter(!is.na(symbol)) ) |> filter(!duplicated(biz_days)) yc
With the curve data prepared, the spotratecurve
is created.
sp_curve <- spotratecurve( yc$r_252, yc$biz_days, "discrete", "business/252", "Brazil/ANBIMA", refdate = refdate ) sp_curve
From the output above it is possible to observe that this curve does not have an interpolation method defined.
Let's, for example, define a flat forward interpolation for this curve.
The FlatForward object is created and set to the curve with the interpolation<-
method.
interpolation(sp_curve) <- interp_flatforward() sp_curve
Now the output shows the curve with the interpolation defined.
[[
The spot rate curve method [[
is used to interpolte the curve.
The term is passed as a Term object or numeric and a spot rate curve is returned with all
interpolated values.
sp_curve[[c(21, 42, 63)]]
The term 21 doesn't exist in the spot rate curve, so it is interpolated according to the interpolation method defined. Since the flat forward interpolation just connect the dots, the terms 42 and 63 have the same values of the spot rate curve.
Other interpolation methods can be set with the interpolation
method overriding any method set
previously.
interpolation(sp_curve) <- interp_naturalspline() sp_curve[[c(21, 42, 63)]]
Set interpolation to NULL
to unset the interpolation.
interpolation(sp_curve) <- NULL sp_curve[[c(21, 42, 63)]]
Note that for those terms in the [[
method that don't have a related term in the spot rate curve,
NA
is returned.
The fixedincome::plot
method for the spot rate curve has an argument use_interpolation
that
shows the interpolation together with the curve points.
This argument defaults to FALSE
.
interpolation(sp_curve) <- interp_flatforward() plot(sp_curve, use_interpolation = TRUE)
Once the interpolation is set, the plot
method uses it to calculate daily forward rates.
Otherwise, it uses the forward rates between the curve terms.
Set the show_forward
argument to TRUE
to show the forward rates.
interpolation(sp_curve) <- NULL plot(sp_curve, show_forward = TRUE, legend_location = "bottomright")
The forward rates are drawn with step lines.
If the use_interpolation
argument is TRUE
then the daily forward rates are calculated with
the defined interpolation.
interpolation(sp_curve) <- interp_flatforward() plot(sp_curve, use_interpolation = TRUE, show_forward = TRUE, legend_location = "bottomright")
It is possible to note that the flat forward daily rates are fairly close to curve terms forward rates.
As the interpolation changes its effects can be viewed in the forward rates dynamic.
interpolation(sp_curve) <- interp_naturalspline() plot(sp_curve, use_interpolation = TRUE, show_forward = TRUE, legend_location = "bottomright")
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